On the Physical Significance of Strong Spatial Dispersion

Optical metamaterials consist of subwavelength inclusions that possess unconventional optical properties that are unavailable in natural materials. The specific shape, composition, and arrangement of these inclusions determine the optical response of the metamaterials. However, designing them for specific applications with traditional simulations and experimental tests is impractical due to their high degree of complexity. To address this, the effective medium theory provides an efficient approach by linking the actual metamaterial to a homogeneous material with specific constitutive relations, allowing it to interact with light in the same manner. Local material laws have been frequently used to model metamaterials as a homogeneous medium, assuming that the electromagnetic response at a point depends solely on the fields at that point. However, the accuracy of these models depends on the characteristic length scale of the metamaterial, which is the ratio between the lattice period and the operational wavelength. When this ratio is not much smaller than one, as is the case with optical metamaterials, spatial nonlocality becomes dominant, and the electromagnetic response of a point is influenced by the fields at many other points within the material. As a result, traditional local material laws cannot accurately describe the behavior of optical metamaterials. To address this challenge, we propose a new approach for modeling the behavior of optical metamaterials using nonlocal material laws. Specifically, we use a Taylor expansion in the Fourier space to approximate a general and exact nonlocal response function of the electric field, allowing us to derive a set of effective material parameters. Our approach accurately captures the spatial nonlocality of optical metamaterials and can be used to design novel and unique optical properties for various applications. In this thesis, firstly, we present two nonlocal models that account for significant spatial dispersion effects and analyze the dispersion behavior of eigenmodes in homogenized metamaterials. We then derive the interface conditions that facilitate the calculation of reflection and transmission coefficients for a homogeneous slab with an incident field. Secondly, to conduct the actual homogenization of a MM, we discuss two methods. The first approach treats the metamaterial as a bulk material and utilizes computational parameter retrieval techniques to assign effective material parameters to the bulk. This technique employs a least-square fitting algorithm to determine the optimal values for the effective material parameters by comparing the reflection and transmission coefficients of the bulk with those of the actual metamaterial. Further, we use this method to study three artificial structures with predetermined scattering properties that are quantified in terms of multipole moments they sustain and reveal that the effective permittivity and permeability are linked to the electric and magnetic dipole moments of the scatterers. Additionally, nonlocal material parameters are related to higher-order multipolar moments and their interaction with dipolar terms. By understanding the significance of each material parameter, we can decide the truncation order for the Taylor expansion of the considered constitutive relations for a given metamaterial. We also investigate the role of the period-to-operational wavelength ratio in homogenizing a metamaterial, specifically an electric dipolar lattice. Surprisingly, we observe a breakdown in homogenization at shorter lattice constants due to near-field interactions among the particles forming the lattice. This suggests that the period should not only be much smaller than the operational wavelength to homogenize a metamaterial but there exists an optimal period for a given inclusion size. The second method introduced in this thesis is a novel homogenization approach using the "effective transition matrix" or $T_{eff}$-matrix, which provides an exact description of the linear interaction between light and the bulk material without the need for any computational retrieval processes. By homogenizing an isotropic 3D metamaterial made of gold nanospheres, we detail the calculation of the corresponding effective material parameters and further obtain the reflection and transmission coefficient for the homogeneous material. The highlight of this approach is the promise to homogenize a 3D metamaterial without requiring a target object as opposed to the case of any parameter retrieval methods. Finally, we summarize all the analytical and numerical results and discuss possible future research endeavors as an extension of the results obtained in the thesis. Overall, the thesis contributes to a deeper understanding of the behavior of optical metamaterials at the effective level and offers valuable insights for future research in this field

Higher order constitutive relations and interface conditions for metamaterials with strong spatial dispersion

To characterize electromagnetic metamaterials at the level of an effective medium, nonlocal constitutive relations are required. In the most general sense, this is feasible using a response function that is convolved with the electric field to express the electric displacement field. Even though this is a neat concept, it bears little practical use. Therefore, frequently the response function is approximated using a polynomial function. While in the past explicit constitutive relations were derived that considered only some lowest order terms, we develop here a general framework that considers an arbitrary higher number of terms. It constitutes, therefore, the best possible approximation to the initially considered response function. The reason for the previously self-imposed restriction to only a few lowest order terms in the expansion has been the unavailability of the necessary interface conditions with which these nonlocal constitutive relations have to be equipped. Otherwise one could not make practical use of them. Therefore, besides the introduction of such higher order nonlocal constitutive relations, it is at the heart of contribution to derive the necessary interface conditions to pave the way for the practical use of these advanced material laws

On the physical significance of non-local material parameters in optical metamaterials

When light interacts with a material made from subwavelength periodically arranged constituents, non-local effects can emerge. They occur because of either a complicated response of the constituents or possible lattice interactions. In lowest-order approximations of a general non-local response function, phenomena like an artificial magnetism and a bi-anisotropic response emerge. However, investigations beyond these lowest-order descriptions of non-local effects are needed for optical metamaterials (MMs) where a significant long-range interaction becomes evident. This highlights the need for additional material parameters to account for spatial non-locality in an effective medium description. These material parameters emerge from a Taylor expansion of the general and exact non-local response function. Even though these non-local parameters improve the effective description, their physical significance is yet to be understood. To improve the situation, we consider a conceptional MM consisting of scatterers characterized by a prescribed multipolar response arranged on a square lattice. Lorentzian polarizabilities describe the scatterers in the electric dipolar, electric quadrupolar, and magnetic dipolar terms. A slab of such a MM is homogenized while considering an increasing number of non-local terms in the constitutive relations at the effective level. We show that the effective permittivity and permeability are linked to the electric and magnetic dipole moments of the scatterers. The non-local material parameters are related to the higher-order multipolar moments and their interaction with the dipolar terms. Studying the effective material parameters with the knowledge of the induced multipolar moments in the lattice facilitates our understanding of the significance of each material parameter. Our insights aid in deciding on the order to truncate the Taylor expansion of the considered constitutive relations for a given MM

Lower limits for the homogenization of periodic metamaterials made from electric dipolar scatterers

Nonlocal constitutive relations promise to homogenize metamaterials even though the ratio of period over operational wavelength is not much smaller than unity. However, this ability has not yet been verified, as frequently only discrete structures were considered. This denies a systematic variation of the relevant ratio. Here, we explore, using the example of an electric dipolar lattice, the superiority of the nonlocal over local constitutive relation to homogenize metamaterials when the period tends to be comparable to the wavelength. Moreover, we observe a breakdown of the ability to homogenize the metamaterial at shorter lattice constants. This surprising failure occurs when energy is transported across the lattice thanks to a well-pronounced near-field interaction among the particles forming the lattice. Contrary to common wisdom, this suggests that the period should not just be much smaller than the operational wavelength to homogenize a metamaterial, but, for a given size of the inclusion, there is an optimal period

Loop Interactions during Catalysis by Dihydrofolate Reductase fromMoritella profunda

Dihydrofolate reductase (DHFR) is often used as a model system to study the relation between protein dynamics and catalysis. We have studied a number of variants of the cold-adapted DHFR from Moritella profunda (MpDHFR), in which the catalytically important M20 and FG loops have been altered, and present a comparison with the corresponding variants of the wellstudied DHFR from Escherichia coli (EcDHFR). Mutations in the M20 loop do not affect the actual chemical step of transfer of hydride from reduced nicotinamide adenine dinucleotide phosphate to the substrate 7,8-dihydrofolate in the catalytic cycle in either enzyme; they affect the steady state turnover rate in EcDHFR but not in MpDHFR. Mutations in the FG loop also have different effects on catalysis by the two DHFRs. Despite the two enzymes most likely sharing a common catalytic cycle at pH 7, motions of these loops, known to be important for progression through the catalytic cycle in EcDHFR, appear not to play a significant role in MpDHFR

A T‐Matrix Based Approach to Homogenize Artificial Materials

The accurate and efficient computation of the electromagnetic response of objects made from artificial materials is crucial for designing photonic functionalities and interpreting experiments. Advanced fabrication techniques can nowadays produce new materials as 3D lattices of scattering unit cells. Computing the response of objects of arbitrary shape made from such materials is typically computationally prohibitive unless an effective homogeneous medium approximates the discrete material. In here, a homogenization method based on the effective transition (T-)matrix, $T_{eff}$ is introduced. Such a matrix captures the exact response of the discrete material, is determined by the T-matrix of the isolated unit cell and the material lattice vectors, and is free of spatial dispersion. The truncation of $T_{eff}$ to dipolar order determines the common bi-anisotropic constitutive relations. When combined with quantum-chemical and Maxwell solvers, the method allows one to compute the response of arbitrarily-shaped volumetric patchworks of structured molecular materials and metamaterials

Protein motions and dynamic effects in enzyme catalysis

The role of protein motions in promoting the chemical step of enzyme catalysed reactions remains a subject of considerable debate. Here, a unified view of the role of protein dynamics in dihydrofolate reductase catalysis is described. Recently the role of such motions has been investigated by characterising the biophysical properties of isotopically substituted enzymes through a combination of experimental and computational analyses. Together with previous work, these results suggest that dynamic coupling to the chemical coordinate is detrimental to catalysis and may have been selected against during DHFR evolution. The full catalytic power of Nature's catalysts appears to depend on finely tuning protein motions in each step of the catalytic cycle

Compassionate use of convalescent plasma for the management of severe pneumonia in critically ill COVID-19 patients-a single center experience, Kerala, India

We assessed treatment effectiveness with convalescent plasma in critically ill COVID-19 pneumonia patients and their association with reduction in C reactive protein level as a sensitive inflammatory marker to the ongoing cytokine storm. Retrospective cohort study based on the detailed electronic medical chart review. The primary outcome was a clinical improvement on day 14, defined as the reduction in cytokine storm as demonstrated by a drop in acute phase reactant C reactive protein; de-escalation from the prior mode of oxygen delivery or not on mechanical ventilation in critically ill COVID-19 patients. C reactive protein was measured by using immunoturbidimetry. IgG antibody against spike protein S1 was measured by chemiluminescent immunoassay. Of 14 patients, all had severe COVID-19 pneumonia [category C], and 9 (64%) were mechanically ventilated soon after the admission into the medical intensive care unit. De-escalation of the oxygenation strategy mode was noted in 11 (79%) patients after convalescent plasma infusion. All patients showed a significant drop in C reactive protein when compared to pre-infusion and post-infusion day 5.  Early compassionate use of convalescent plasma with higher titters of IgG antibodies against S1may positively benefit the overall outcome in critically ill COVID-19 patients with severe pneumonia

Effectiveness of deep neural networks in hearing aids for improving signal-to-noise ratio, speech recognition, and listener preference in background noise

IntroductionTraditional approaches to improving speech perception in noise (SPIN) for hearing-aid users have centered on directional microphones and remote wireless technologies. Recent advances in artificial intelligence and machine learning offer new opportunities for enhancing the signal-to-noise ratio (SNR) through adaptive signal processing. In this study, we evaluated the efficacy of a novel deep neural network (DNN)-based algorithm, commercially implemented as Edge Mode™, in improving SPIN outcomes for individuals with sensorineural hearing loss beyond that of conventional environmental classification approaches.MethodsThe algorithm was evaluated using (1) objective KEMAR-based performance in seven real-world scenarios, (2) aided and unaided speech-in-noise performance in 20 individuals with SNHL, and (3) real-world subjective ratings via ecological momentary assessment (EMA) in 20 individuals with SNHL.ResultsSignificant improvements in SPIN performance were observed on CNC+5, QuickSIN, and WIN, but not NST+5, likely due to the use of speech-shaped noise in the latter, suggesting the algorithm is optimized for multi-talker babble environments. SPIN gains were not predicted by unaided performance or degree of hearing loss, indicating individual variability in benefit, potentially due to differences in peripheral encoding or cognitive function. Furthermore, subjective EMA responses mirrored these improvements, supporting real-world utility.DiscussionThese findings demonstrate that DNN-based signal processing can meaningfully enhance speech understanding in complex listening environments, underscoring the potential of AI-powered features in modern hearing aids and highlighting the need for more personalized fitting strategies